# Explain how speed is a rate of change?

Xavier is running a marathon. At time $t = 0$ hours, he is $0$ miles from the start. At time $t = 5$ hours, he is $26$ miles from the start. His average speed throughout the whole race is the distance he traveled over the time it took. So:
Average speed $= \frac{26}{5}$.
His speed is essentially the rate at which his position changes. If his rate is $\frac{26}{5}$, his position changes by $\frac{26}{5}$ miles every hour.